Two Squares and a Circle- March 6-10, 1995 Corey and Vernon were hanging out in the Mac lab when Muzz came in, looking excited.
"Check this out! It's another problem for us. My mom got it from some kid she tutors. His teacher calls it the problem of the day or something, and this one was geometry."
"Great," said Corey. "We're almost done with this trig project, so let's see it."
"Okay.
You have a circle and two squares. One square has the diameter of the circle as an edge. The other square in inscribed in the circle. What's the area of the small square compared to the big one?""Hey, no problem," boasted Vernon. "I can do that. Remember how fast I got the last one?"
"We don't need a history lesson," said Muzz.
"It's not like I'm telling you Elvis is dead, man," said Vernon. "I'm just reminding you I'm on top of this stuff."
"Okay, if you think you're so quick, there's a second part to the problem," countered Muzz.
"In the first part, the second square was inscribed in the whole circle. Now, what if the second square is inscribed in the semi-circle? Then how do the areas of the squares compare?"
- Daniel Gabriel, Akiba Hebrew Academy
- Avi Klein, Akiba Hebrew Academy
- Charles Floyd and Indira Sarma, Woodward Academy
- Kim Carbone, Fairfield HS
- Cecilia Merediz, Fairfield HS
- Arpan Munier, Fairfield HS
- Brad Warner, Fairfield HS
- Ruth Carver's Geometry class, Mount St. Joseph,
- Mr. Gehrett's 7th Period Geometry Class, Ridgeview HS
- Mr. Gehrett's 2nd Period Geometry Class, Ridgeview HS
Correct solutions to the problem were submitted by:
The following students (classes!) submitted correct solutions to the first part, but not the second. The classes' solutions are included in their entirety - see if you can find where they went wrong.
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